At least 30 people were killed in fresh clashes in the northern state of Yobe on Wednesday, a police source said.
Wednesday's violence came after the army shelled a mosque and the home of Mohammed Yusuf, the group's alleged leader, in Maiduguri, which is the capital of Borno state.
"We are not sure whether he has been killed in the shelling or has managed to escape," a police officer said of Yusuf.
Boko Haram opposes Western-style education and has said it wants to lead an armed insurrection and rid society of "immorality" and "infidelity".
Umaru Yar'Adua, Nigeria's president, has vowed that the group will be hunted down and punished.
He said that the military operation currently under way would "contain them once and for all" and that "they will be dealt with squarely and forthwith".
Before leaving on a trip to Brazil on Tuesday, Yar'Adua said that the situation was "under control".
But fresh fighting broke out in Maiduguri following the assault on the home of Yusuf.
Dozens of people took shelter from the bombardment in a local police station.
"It is the first time in my life that I hear this kind of mortar shelling," said one man, who had taken cover there, along with his wife and three daughters.
"I thought they targeted my house."
An AFP correspondent reported witnessing soldiers shooting three young men dead at point blank range close to the city's police headquarters.
The men, who had just been arrested, were seen kneeling and pleading for their lives before being shot.
Al Jazeera's Yvonne Ndege, reporting from Nigeria's capital, Abuja, said there had been an intensification of the assault on members of Boko Haram.
She said the president had made it clear that those caught perpetrating violence or working with the fighters would be killed.
Boko Haram, which means "Western education is prohibited" in the local Hausa dialect, has called for the enforcement of sharia or Islamic law, across Africa's most populous nation.
Nii Akuetteh, the founder of the Democracy and Conflict Research Institute, an African think-tank, told Al Jazeera that, while religious clashes had occurred in the past in Nigeria, the recent clashes appeared to have little political motivation.
"Previously when you had religion rear its head in politics [in Nigeria] you had a clash between Christians mainly in the south and Muslims in the north.
"I think that one you have to talk of the political implications of that, but the most recent, frankly, it seems to me is nothing but religious extremism and violence."
Nigeria's 140 million people are nearly evenly divided between Christians, who dominate the south, and the primarily northern-based Muslims.
Islamic law was implemented in 12 northern states after Nigeria returned to civilian rule in 1999 following years of military rule.
Akuetteh also said that poverty, which has sparked conflict elsewhere in Nigeria, mainly in the oil-rich Niger delta, was not a contributing factor.
"I think religious politicisation of religion in Nigeria is separate and apart from the poverty that is there.
"I would look more to religious prejudice and extremists wanting to inject religion into politics rather than poverty per se."
The clashes began on Sunday in nearby Bauchi state, with fighters attacking police stations, before spilling over into Yobe.
Residents said fighters armed with machetes, knives, bows and arrows and home-made explosives, attacked police buildings and anyone resembling a police officer or government official in the city.
But most of the casualties appear to have been in Maiduguri, the northeastern city known as the birthplace and stronghold of the group.